Question

Hope has placed a bunch of marbles (half red, half green) in a bag and wants Allan to select one at random. If Allan pulls out a marble, records the color, replaces it, and repeats this 100 times, which of the following is true?

(A) It is unlikely Allan will choose red more than 50 times.
(B) If Allan draws 10 green marbles in a row, the next one is guaranteed to be a red marble.
(C) The overall proportion of red marbles drawn should be close to 0.50
(D) The chance that the 100th draw will be red depends on the results of the first 99 draws.
(E) All of the above are true.

Answer 1

Answer: E) all of the above

Explanation: each one works

Answer 2

The correct answer is (C), as the overall proportion of red marbles drawn should approximate 0.50 since each draw is an independent event with equal probability for red and green marbles.

Step-by-step explanation:

The question addresses the concepts of probability and randomness in mathematics, specifically related to the action of drawing marbles from a bag at random with replacement.

The correct answer to the student's question is (C) The overall proportion of red marbles drawn should be close to 0.50. This is because each draw is an independent event, and since the bag contains an equal number of red and green marbles, the probability of drawing a red marble is 0.50 on each draw.

Option (A) is incorrect because it is quite likely that Allan will choose red around 50 times, due to the probability of choosing a red marble being 0.50 each time. Option (B) is incorrect because previous draws have no impact on subsequent draws; every draw is independent, and the probability remains the same each time. Option (D) is also incorrect for the same reason: the result of the 100th draw is independent of the previous 99 draws.